Several peaks of total current in Trichel pulse
The numerical simulations of negative corona at constant voltage in Trichel pulse mode are carried out in assumptions of presence and absence of photoemission from cathode. In absence of photoemission two peaks of total current or the step before the main peak were obtained for very small values of...
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nasplib_isofts_kiev_ua-123456789-822472025-02-09T09:38:14Z Several peaks of total current in Trichel pulse Кілька піків повного струму в імпульсі Тричела Несколько пиков полного тока в импульсе Тричела Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Низкотемпературная плазма и плазменные технологии The numerical simulations of negative corona at constant voltage in Trichel pulse mode are carried out in assumptions of presence and absence of photoemission from cathode. In absence of photoemission two peaks of total current or the step before the main peak were obtained for very small values of ion-electron emission coefficient. In presence of photoemission there were observed several maximums, connected with instability development of the process based on radiation of photons, photoemission, and avalanche multiplication. Выполнено численное моделирование отрицательной короны при постоянном приложенном напряжении в режиме импульсов Тричела в предположениях наличия и отсутствия фотоэмиссии с катода. При отсутствии фотоэмиссии два пика полного тока или ступенька перед основным пиком были получены при очень малых значениях коэффициента ионно-электронной эмиссии. При наличии фотоэмиссии наблюдалось несколько максимумов, связанных с развитием неустойчивости процесса, основанного на излучении фотонов, фотоэмиссии и размножении лавин. Виконано числове моделювання негативної корони при постійній докладеній напрузі в режимі імпульсів Тричела в припущеннях наявності та відсутності фотоемісії з катода. За відсутності фотоемісії два піки повного струму або сходинка перед основним піком були отримані при дуже малих значеннях коефіцієнта іонно-електронної емісії. За наявності фотоемісії спостерігалося кілька максимумів, пов’язаних з розвитком нестійкості процесу, який ґрунтується на випромінюванні фотонів, фотоемісії та розмноженні лавин. 2015 Article PACS: 52.80.Hc https://nasplib.isofts.kiev.ua/handle/123456789/82247 en Вопросы атомной науки и техники application/pdf |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. Several peaks of total current in Trichel pulse Вопросы атомной науки и техники |
| description |
The numerical simulations of negative corona at constant voltage in Trichel pulse mode are carried out in assumptions of presence and absence of photoemission from cathode. In absence of photoemission two peaks of total current or the step before the main peak were obtained for very small values of ion-electron emission coefficient. In presence of photoemission there were observed several maximums, connected with instability development of the process based on radiation of photons, photoemission, and avalanche multiplication. |
| format |
Article |
| author |
Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_facet |
Bolotov, O. Golota, V. Kadolin, B. Mankovskyi, S. Ostroushko, V. Pashchenko, I. Taran, G. Zavada, L. |
| author_sort |
Bolotov, O. |
| title |
Several peaks of total current in Trichel pulse |
| title_short |
Several peaks of total current in Trichel pulse |
| title_full |
Several peaks of total current in Trichel pulse |
| title_fullStr |
Several peaks of total current in Trichel pulse |
| title_full_unstemmed |
Several peaks of total current in Trichel pulse |
| title_sort |
several peaks of total current in trichel pulse |
| publishDate |
2015 |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
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https://nasplib.isofts.kiev.ua/handle/123456789/82247 |
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Вопросы атомной науки и техники |
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ISSN 1562-6016. ВАНТ. 2015. №1(95)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 243-245. 243
SEVERAL PEAKS OF TOTAL CURRENT IN TRICHEL PULSE
O. Bolotov, V. Golota, B. Kadolin, S. Mankovskyi, V. Ostroushko, I. Pashchenko, G. Taran,
L. Zavada
NSC “Kharkov Institute of Physics and Technology” Kharkov, Ukraine
E-mail: ostroushko-v@kipt.kharkov.ua
The numerical simulations of negative corona at constant voltage in Trichel pulse mode are carried out in
assumptions of presence and absence of photoemission from cathode. In absence of photoemission two peaks of
total current or the step before the main peak were obtained for very small values of ion-electron emission
coefficient. In presence of photoemission there were observed several maximums, connected with instability
development of the process based on radiation of photons, photoemission, and avalanche multiplication.
PACS: 52.80.Hc
INTRODUCTION
In some experimental conditions, a total current time
dependence of one Trichel pulse in negative corona has
several maximums [1]. Formerly, the numerical
simulations were carried out for one-dimensional
particle distribution with the field corresponding to
disks [2, 3], and for three-dimensional axially
symmetric model [4]. There were accounted ion-
electron emission (in [2-4]) and photoemission (in [2]).
Two peaks were obtained in [2] and [3]. In [2], the first
peak is accompanied with intensive photoemission, and
the second with ion-electron emission. In [3], at
cathode, the first peak corresponds to displacement
current maximum and is connected with ionization
wave, and the second peak corresponds to conduction
current maximum. In [4], total current has one
maximum, although there is observed the propagation of
ionization wave in the space near cathode. The time
between peaks obtained in simulations was too large, in
comparing with one obtained in the experiment [1].
The explanation proposed in [1], in which decisive
role belongs to ionization wave, does not indicate
clearly the causes of total current decrease between its
maximums. The results of numerical simulations
suggest two possible causes of this decrease. One cause
is connected with decay of fast ionization wave. A new
increase of total current after wave decay may be
connected with comparatively slow increase of ion
current at cathode or with field strengthening and
ionization rate increase near transverse ends of plasma
region in consequence of transverse expansion of
ionization wave. Another cause of total current
oscillations is connected with instability of the process
based on radiation of photons, photoemission, and
impact ionization.
1. IONIZATION WAVE AND ION CURRENT
In simulations carried out without photoemission
account, the pulses with two peaks of total current, and,
also, the pulses with a step before single peak were
obtained in two different assumptions about ion
mobility dependence on electric field strength. Namely,
the strength increase may cause increase or decrease of
the mobility. Two peaks were obtained with the
decrease and the step with the increase. The current
increase before the first peak or the step was connected
with development of ionization wave. The second and
single peaks were connected with intensive going out of
ions to cathode.
Near-cathode ionization wave is somewhat similar to
streamer, but neighborhood of needle cathode leads to
some differences of the wave from cathode directed
streamer, developing in the mid-space far from the
needle. Great field strength near head of the streamer is
caused by great charge of the head, and farther from the
head the strength is less. Like the streamer, the wave is
accompanied with forming of plasma region and
increase of field strength near some side of the plasma
region up to the values characteristic for streamer. But
field strength increases in the whole space between the
plasma region and cathode, and strength is greater in the
space nearer to cathode. After formation, the plasma
region is expanding to cathode, and approximately the
same voltage drop between the plasma region and
cathode is becoming correspondent to the decreasing
distance. So, in the space between the plasma region
and cathode, the field strength and ionization coefficient
increase, and to do the same number of ionization acts
an electron needs the shorter drift path. Finish of such
drift with ionizations corresponds to entering of the
electron into the end of plasma region nearer to cathode
with plasma forming in this place. In the stronger field
such drift is finished at the nearer distance from
cathode. After the strength increase up to the values, at
which ionization coefficient depends on the strength
faintly, the development of the described ionization
wave is considerably slowing down, and displacement
current considerably decreases, leading to some
decrease of total current.
As field near cathode is not uniform, in the different
areas over the cathode surface the wave develops with
different rates. The developing is slower in the weaker
field farther in the direction transverse to the field
strength. So, the process gets the form of transverse
ionization wave expansion after considerable slowing
down of its expansion along the field strength. The
written above may be illustrated by Fig. 1, where
electron distribution near cathode is shown towards the
ends of the longitudinal and transverse ionization wave
expansions. It was obtained in assumption of ion
mobility decrease with field strength increase.
The second peak may arise in connection with going
out of positive ions to cathode. Development of
avalanches, starting by electrons from cathode, yields
244 ISSN 1562-6016. ВАНТ. 2015. №1(95)
steep ion density increase with the distance from
cathode. Going out of such distribution to cathode leads
to increase of conduction current at cathode, which is
the main part of the total current at this time. After the
going out of the main part of the formed positive ions,
the total current decreases.
Fig. 1. Electron density near cathode towards the ends
of longitudinal and transverse ionization wave
expansions (time difference 28 ns) in assumption of ion
mobility decrease with field strength increase; densities
are logarithmically distinguished by color (range at the
top) in interval … cm
; in the total current
time dependence in corner the instant is marked
Fig. 2. Density of positive ions at the beginning of going
out of their main part to cathode in assumption of ion
mobility increase with field strength increase; densities
are logarithmically distinguished by color in interval
… cm
If ion mobility in strong field is sufficiently large
then considerable increase of conduction current at
cathode may take place at the time of considerable
slowing down of the ionization wave longitudinal
expansion, and instead of minimum between two peaks
of total current it is formed somewhat similar to the step
before the main peak. Such case is illustrated in Fig. 2
by positive ion distribution at the beginning of going out
of their main part to cathode (and total current step
formation). It was obtained in assumption of ion
mobility increase with field strength increase.
The simulations yielded two peaks of total current
only for the values of ion-electron emission coefficient
considerably less than the usually taken values
10
…10
. On the value of the coefficient, it depends
how far from cathode the considerable slowing down of
ionization wave takes place. For the larger coefficient, it
takes place nearer to cathode, in connection with greater
electron flow from cathode. To come to cathode from
there, the ions need less time, and two peaks may be
transformed to single peak, as it took place in
simulations [4].
2. OSCILLATIONS WITH PHOTOEMISSION
If photoemission is considerable then even a few
peaks of total current may be formed, in connection
with two effects: (1) enlarging of ionization rate in the
part of space and photon radiation from there when
electric field strength there increases, (2) increase of the
strength in front of bunch of electrons, which have been
knocked out from cathode by photons and are moving to
anode. Oscillations may be found out even only on the
base of photon radiation from discharge space and
photoemission from cathode. Let us consider the model,
in which only two spaces are accounted: the space c
near cathode, and the space b somewhat farther from
cathode. The process may be described with the
equations
t b c c b bN N N ,
t ( , ) ( , )c c c b c b c b b c cN f N N N f N N N N .
Here
t is time derivative, the indexes c and b
indicate the spaces,
x is reciprocal to the characteristic
time of electron removing from the space x , where x
stands for c or b ,
xN is electron density,
xf is photon
generation frequency. Let us put
0 1 exp( )x x xN N N t , where the indexes 0 and 1
indicate a stationary value and a small perturbation. Let
us use the designations (0)
xf , (1)
xcf , (1)
xbf , respectively,
for the values of ( , )x c bf N N , ( ) ( , )c x c bN f N N ,
( ) ( , )b x c bN f N N at {
0c cN N ,
0b bN N }. Let us
put (1) (0) (1) (1)
0 0x x c cx b bxf f N f N f , (1)
b c cA f ,
(1) 2 (1)( ) 4c c b c bB f f . For stationary values,
one gets the equations
0 0c c b bN N and
(0) (0)
0 0( )c c c b bf N f N , and the condition
(0) (0)
c b b c c bf f of their nonzero solution
existence. For linear perturbations, one gets the
equations (1) (1)
1 1( )c c c b bf N f N and
1 1( )b b c cN N , and the condition 2(2 )A B .
The inequality 0A means instability, and 0B
means oscillations. It is assumed that (1) 0cbf , (1) 0bbf ,
(1) 0ccf , and (1) 0bcf , according to influence of the
negative charge disposition on the field in relevant
spaces. For instability, the inequality
(0) (1) (1)
0 0c b bc b c c ccf N f N f should be held.
Oscillations correspond to the inequality
ISSN 1562-6016. ВАНТ. 2015. №1(95) 245
(1) (1) (0)
0 0
(0) (1) (1) 2
0 0
4 ( ) 4
( )
c c cb b bb c b
c b bc b c c cc
N f N f f
f N f N f
.
In particular, if the value of (1)
bcf is sufficiently large
then the process is unstable. And, for the given (1)
bcf , if
the values of (1)| |cbf and (1)| |bbf are sufficiently large
then the instability is oscillatory.
Fig. 3. The rates of the field strength changes separated
with time 0.5 ns; the rates are linearly distinguished by
color from - V ·cm
·s
to V ·cm
·s
With impact ionization, the instability may be
considerably enhanced due to electron multiplication.
Intervals between maximums correspond to the time of
electron drift from cathode to the space of intensive
photon radiation near the plasma region. This time is
considerably less than the time of positive ion drift from
plasma region to cathode, and it corresponds to the time
between peaks of total current obtained in experiment
[1]. In Fig.3, the rates of field strength change are
shown for two instants, which belong to time intervals
of total current slow change and rapid increase. Time
derivative of field strength in the space near the
transverse ends of plasma region is positive, which is
partially connected with ionization wave expansion in
this direction. But from time to time the rate of strength
change there increases additionally, due to the next
approach of the increased number of electrons, which
were obtained as consequence of the previous approach,
through the increase of photon radiation from the space,
electron emission from cathode, and electron
multiplication in avalanches. The field near the plasma
region is not so strong as one near the cathode surface,
the photon generation frequency there is less, but
sensitivity of the frequency to the field strength value is
higher, and the greater (through multiplication) number
of electrons compensates the smaller frequency, so that
comparatively small oscillations of the field strength
near the plasma region yield considerable oscillations of
total current.
CONCLUSIONS
In Trichel pulse mode of negative corona, during
transition from simple avalanche multiplication to
ionization wave set up, the total current usually changes
monotonously without any temporary decreases. Several
total current maximums with time intervals of order of
nanosecond obtained in experiments, probably, are
connected with instability of the process based on the
photon radiation from discharge space, photoemission
from cathode, and electron multiplication due to impact
ionization. The first maximum is connected with
considerable slowing down of longitudinal expansion of
ionization wave.
REFERENCES
1. M. Černak, T. Hosokawa, S. Kobayashi, T. Kaneda.
Streamer mechanism for negative corona current pulses //
Journal of Applied Physics. 1998, v. 83, № 11, p. 5678-5690.
2. R. Morrow. Theory of stepped pulses in negative
corona discharges // Physical Review A. 1985, v. 32,
№ 6, p. 3821-3824.
3. A.P. Napartovich, Yu.S. Akishev, A.A. Deryugin,
I.V. Kochetov, M.V. Pan’kin, N.I. Trushkin. A
numerical simulations of Trichel pulse formation in a
negative corona // Journal of Physics D: Applied
Physics. 1997, v. 30, p. 2726-2736.
4. Yu.S. Akishev, I.V. Kochetov, A.I. Loboiko,
A.P. Napartovich. Numerical simulations of Trichel
pulses in a negative corona in air // Plasma Physics
Reports. 2002, v. 28, № 12, p .1049-1059.
Article received 20.10.2014
НЕСКОЛЬКО ПИКОВ ПОЛНОГО ТОКА В ИМПУЛЬСЕ ТРИЧЕЛА
О. Болотов, В. Голота, Б. Кадолин, С. Маньковский, В. Остроушко, И. Пащенко, Г. Таран, Л. Завада
Выполнено численное моделирование отрицательной короны при постоянном приложенном напряжении
в режиме импульсов Тричела в предположениях наличия и отсутствия фотоэмиссии с катода. При
отсутствии фотоэмиссии два пика полного тока или ступенька перед основным пиком были получены при
очень малых значениях коэффициента ионно-электронной эмиссии. При наличии фотоэмиссии наблюдалось
несколько максимумов, связанных с развитием неустойчивости процесса, основанного на излучении
фотонов, фотоэмиссии и размножении лавин.
КІЛЬКА ПІКІВ ПОВНОГО СТРУМУ В ІМПУЛЬСІ ТРИЧЕЛА
О. Болотов, В. Голота, Б. Кадолін, С. Маньковський, В. Остроушко, І. Пащенко, Г. Таран, Л. Завада
Виконано числове моделювання негативної корони при постійній докладеній напрузі в режимі імпульсів
Тричела в припущеннях наявності та відсутності фотоемісії з катода. За відсутності фотоемісії два піки
повного струму або сходинка перед основним піком були отримані при дуже малих значеннях коефіцієнта
іонно-електронної емісії. За наявності фотоемісії спостерігалося кілька максимумів, пов’язаних з розвитком
нестійкості процесу, який ґрунтується на випромінюванні фотонів, фотоемісії та розмноженні лавин.
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